Question

Three different substances have their specific heats in the ratio 2 : 3 : 1 and their temperatures are increased in the ration 3 : 1: 2 respectively. If same heat is supplied to these substances, find the ratio of their masses.

Answer 1

We know, Heat supplied to the substance, $Q=ml$, where $m$ is mass of the substance and $l$ is the latent heat.

We also know, $l=C\times \Delta T$, where $C$ is the specific heat and $\Delta T$ is temperature increase.

Hence, $Q=mC\Delta T$,

or, $m=\frac{Q}{C\Delta T}$

So the ratio of masses is

$\frac{Q}{C_1\Delta T_1}:\frac{Q}{C_2\Delta T_2}:\frac{Q}{C_3\Delta T_3}⟹\frac{1}{6}:\frac{1}{3}:\frac{1}{2}$